Question
Which equation shows the process of standardizing? \( \begin{array}{l}E(X)=n p \\ Z=(X-\mu) / \sigma \\ f(x)=1-(\sigma / \mu) \\ E(X)=\mu\end{array} \)
Ask by Ortega Kelley. in the United States
Mar 10,2025
Upstudy AI Solution
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Answer
The equation that shows the process of standardizing is:
\[
Z = \frac{X - \mu}{\sigma}
\]
Solution
1. The process of standardizing involves transforming a random variable \( X \) into a standard score \( Z \) by subtracting the mean \( \mu \) and dividing by the standard deviation \( \sigma \).
2. The equation that represents this process is:
\[
Z = \frac{X - \mu}{\sigma}
\]
3. Evaluating the other options:
- \( E(X) = np \) represents the expected value of a binomial variable but does not show standardizing.
- \( f(x) = 1 - \frac{\sigma}{\mu} \) is not related to standardizing.
- \( E(X) = \mu \) simply reiterates the definition of the mean.
Thus, the equation that shows the process of standardizing is:
\[
Z = \frac{X - \mu}{\sigma}
\]
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Simplify this solution Bonus Knowledge
The equation that shows the process of standardizing is \( Z=(X-\mu) / \sigma \). This formula transforms a raw score \( X \) from any normal distribution to a standard score (Z-score), allowing for comparison across different datasets, regardless of their original means or standard deviations. Standardization is widely used in various fields like psychology, education, and finance to normalize scores for better analysis. For example, in standardized testing, converting raw scores to Z-scores can provide a clearer understanding of a student's performance relative to their peers, helping educators pinpoint strengths and weaknesses effectively.
